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This is probably a dumb question but I'm stuck. So here goes:

The dimensions of a plot of land are in a 3:4 ration. If the area of the plot of land measures 1072 m^2 and is also surrounded by a uniform walkway that has a width of 2m. Find the dimensions of the plot of land. Find the area of the whole plot of land, including the walkway.

So far all I got was this 3x * 4y = 1072 and (3x + 2)(4y + 2) is equal to the area of the whole thing. I've tried everything with this, and I just can't figure it out, I've done problems like this before, but it has been so long that I don't remember what to do when they don't give you the length and width.

Argus
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    One step at a time. Let the dimensions be $3x$ and $4x$. We are told that $(3x)(4x)=1072$. From this we can find $x$. (Are you sure about the numbers? Usually they are arranged to turn out more nicely.) Now you know the size of the plot of land, and can find the rest. Note that you will be adding $4$ metres to the dimensions, not $2$, because the walkway goes all the way around. – André Nicolas Apr 03 '14 at 01:46
  • Yeah I'm sure about the numbers, I thought they were weird too. Actually I made a small mistake, its supposed to be 3x * 4y – Argus Apr 03 '14 at 01:50
  • Another way, more or less the same, but involving fractions, is let the long side be $y$. Then the short side is $\frac{3y}{4}$. So we get $\frac{3y^2}{4}=1072$. solve for $y$. – André Nicolas Apr 03 '14 at 01:57
  • Well that's probably what will work best, I still ended up getting a horrible number. Wish I could pick this as the answer. – Argus Apr 03 '14 at 02:11
  • There is a perfectly good answer available. It may be that you are expected to give the dimensions say to the nearest cm, in which case you can turn to the calculator. – André Nicolas Apr 03 '14 at 02:13

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The ratio $\mbox{width:length}=3:4$, and hence we may assume for some constant $x$, $\mbox{width}=3x,\mbox{length}=4x$, giving: $$3x\cdot4x=1072\\ \implies x=\sqrt{\dfrac{1072}{12}}\mbox{ m}$$ Thus, $$(3x+4)(4x+4)=12x^2+12x+16x+16=\left(1072+28\sqrt{\dfrac{1072}{12}}+16\right)\mbox{ m}^2$$